Combining Down and Up (Final answers)

After both passes, every node $v$ has two values. down[v] captures everything in $v$'s subtree. up[v] captures everything outside $v$'s subtree. The final answer for node $v$ as root combines these two.

For sum-of-distances, the formula is answer[v] = down[v] + up[v]. For max-depth problems, it might be answer[v] = max(down[v], up[v]). The combine function depends on the problem, but the two-pass structure stays the same.

This gives you all $n$ answers in $O(n)$ total time and $O(n)$ space. No recomputation needed.